You can ask Three Dog for directions to the Museum of Technology and the Washington Monument. From the radio studio, where you met Three Dog, proceed downstairs to the back door of the Galaxy News Radio building. From there you will need to locate the entrance to the Collapsed Car Tunnel. From the back door of GNR, you can see a bus below and to the right. The entrance is to the right of the bus. You may also notice some Feral Ghouls roaming around the bus. Cross the bridge on the left and turn right to find some loot at the picnic table, then you can jump down onto the bus.
Enter the Collapsed Car Tunnel door and follow the tunnels to Dupont Station. Enter Dupont Station and follow the waypoints south, while staying on the Red Metro line. You will pass the Central Station and then later reach the Museum of Technology. During this trip you will encounter lots of Raiders, Feral Ghouls and a few Super Mutants, so make sure you have plenty of Stimpacks, ammo and weapons. See Metro for detailed directions.
Find the Washington Monument
Exit the Museum and head west for the Washington Monument. It is also in The Mall area and can be seen from the entrance of the Museum of Technology as a giant obelisk. There are Brotherhood guards stationed there and you'll need to use the terminal to open the security doors. The password is given to you in your notes at the beginning of the quest. Take the elevator to the top and interact with the radio equipment to install the dish. Finally, return to Three Dog at Galaxy News Radio to finish the quest.